I've noticed that these kinds of rhythms seem to be extremely common in popular music:
X: 1 M: 4/4 L: 1/16 K: C c3c3c2 c3c3c2|c3c3c3c3c2c2|
The example in the first bar appears to be a 2 over 3 polyrhythm followed by an eighth note, and the second bar is a 4 over 3 polyrhythm followed by two eighth notes.
I've been told that hemiola describes any 2 against 3 polyrhythm, but this doesn't "feel" like one to me, since I've almost always seen it used to refer to this kind of rhythm instead:
X: 2 M: 9/8 K: Fm alto (L=B=A)(L^G =G)(L^F=F) (L=E/^D/=D/C/=B,/=A,/)|
X: 3 M: 3/4 L: 1/4 K: Fm alto z [C,CAf] z | [C,CAf] z [C,CAf] |
In these examples (from Tchaikovsky's 4th), 3 notes are played in the space of 2, rather than 2 (or 4) in the space of 3.
Could the latter case also be referred to as hemiola? If not, does it have a standard name in general? Since the particular arrangements of 3-3-2 and 3-3-3-3-2-2 (shown above) are so common, do they have a specific name as well?